OFFSET
1,2
FORMULA
E.g.f.: A(x) = log(B(x)), where B(x) is e.g.f. of A138860.
E.g.f.: A(x) = Series_Reversion[ 2*x/(exp(x) + exp(2*x)) ].
a(n) ~ n^(n-1)*(1+r)^n*r^n/(sqrt(1+3*r)*(1-r)^(2*n)*exp(n)*2^n), where r = 0.6472709258412625... is the root of the equation (r/(1-r))^(1+r) = e. - Vaclav Kotesovec, Jun 15 2013
MAPLE
A138903 := proc(n) local k ; add(binomial(n, k)*(n+k)^(n-1), k=0..n)/2^n ; end: seq(A138903(n), n=1..20) ; # R. J. Mathar, Apr 12 2008
MATHEMATICA
Table[1/2^n * Sum[Binomial[n, k]*(n+k)^(n-1), {k, 0, n}], {n, 1, 20}] (* Vaclav Kotesovec, Jun 15 2013 *)
PROG
(PARI) {a(n)=local(X=x+x*O(x^n)); n!*polcoeff(serreverse(2*x/(exp(X)+exp(2*X)) ), n)}
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul D. Hanna and Vladeta Jovovic, Apr 02 2008, Apr 03 2008
EXTENSIONS
More terms from R. J. Mathar, Apr 12 2008
STATUS
approved